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On the existence of para-orthogonal rational functions on the unit circle
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Adhemar Bultheel
Published/Copyright:
July 26, 2010
Abstract
Similar as in the classical case of polynomials, as is known, para-orthogonal rational functions on the unit circle can be used to obtain quadrature formulas of Szegő-type to approximate some integrals. In the present paper we carry out a thorough discussion of the existence of such rational functions in terms of the underlying Borel measure on the unit circle.
Keywords: para-orthogonal rational functions; orthogonal rational functions; Rrproducing kernels; finite Borel measures on the unit circle
Published Online: 2010-07-26
Published in Print: 2010-07
© by Oldenbourg Wissenschaftsverlag, Heverlee (Leuven), Germany
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Keywords for this article
para-orthogonal rational functions;
orthogonal rational functions;
Rrproducing kernels;
finite Borel measures on the unit circle
Articles in the same Issue
- On a modification of Wong´s asymptotic expansion of the Kontorovich–Lebedev transform
- Regularity results for generalized electro-magnetic problems
- Neck pinching for periodic mean curvature flows
- Zur Regularität von drei Integralen im Hilbertraum
- Generalized radon transform on the sphere
- Local behavior of smooth functions for the energy Laplacian on the Sierpinski gasket
- On the existence of para-orthogonal rational functions on the unit circle
